The essential
Four three-axis load cells, A, B, C and D, sit at the corners of a rectangle of width W and length L between a platform and the ground. Each net force is the sum of the four readings in its direction. Each net moment is a signed combination of the readings, multiplied by half the spacing, W/2 or L/2. The method holds only if the platform is stiff enough that each load cell sees forces and no local moment.
What is assumed?
The platform assembly is stiff enough that each load cell carries only forces, with no local moment. All the moments on the platform are then reacted by the three forces measured at each load cell.
How are the net forces calculated?
Each net force is the sum of the four readings in that direction.
- Fx = fxA + fxB + fxC + fxD
- Fy = fyA + fyB + fyC + fyD
- Fz = fzA + fzB + fzC + fzD
How are the net moments calculated?
From signed combinations of the readings, about the center point of the plane defined by the sensing origins of the four load cells. Roll and pitch come from the vertical readings; yaw comes from the horizontal ones. The result includes the free moment of any force couple acting on the platform. The signs depend on where A, B, C and D sit: follow the diagram of the note.
- Mx, roll: the differences of the fz readings across the width, times W/2.
- My, pitch: the differences of the fz readings along the length, times L/2.
- Mz, yaw: the differences of the fy readings times L/2, plus those of the fx readings times W/2.
Where is the sensing origin?
The sensing origin depends on the load cell model, and W and L are measured between these points. On some models it is essentially the center of the top fastening surface.
The technical note
One page, with the layout of the four load cells and the equations with their signs.
To remember
- Forces: sum the four readings in each direction.
- Moments: signed differences between cells, times W/2 or L/2.
- The platform must be stiff: no local moment into a load cell.